Abstract
A near-Heyting algebra is a join-semilattice with a top element such that every principal upset is a Heyting algebra. We establish a one-to-one correspondence between the lattices of filters and congruences of a near-Heyting algebra. To attain this aim, we first show an embedding from the lattice of filters to the lattice of congruences of a distributive nearlattice. Then, we describe the subdirectly irreducible and simple near-Heyting algebras. Finally, we fully characterize the principal congruences of distributive nearlattices and near-Heyting algebras. We conclude that the varieties of distributive nearlattices and near-Heyting algebras have equationally definable principal congruences.
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Presented by M. Ploščica
This work was partially supported by Universidad Nacional de La Pampa (Facultad de Ciencias Exactas y Naturales) under the Grant P.I. 64 M, Res. 432/14 CD. The first author was also partially supported by CONICET under the Grand PIP 112-20150-100412CO.
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González, L.J., Lattanzi, M.B. Congruences on near-Heyting algebras. Algebra Univers. 79, 78 (2018). https://doi.org/10.1007/s00012-018-0560-6
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DOI: https://doi.org/10.1007/s00012-018-0560-6